June 24, 2007
June 24, 2007
June 27, 2007
12.1206.1 - 12.1206.15
Promoting Holistic Problem-Solving in Mechanics Pedagogy
The authors propose three strategies that are designed to enhance students’ understanding and problem-solving ability in introductory mechanics courses: (1) employing multiple- method problem-solving, in which students solve a given problem using more than one method; (2) organizing systems of linear equations into a standard “tabular” format which resembles matrix format; and (3) emphasizing the discussion and use of assumptions in problem-solving activities. The authors give a rationale for each strategy, present a review of several mechanics textbooks to determine the prevalence of these strategies, and provide local student performance data that, while as yet inconclusive, suggests a possible method for assessment of the strategies’ efficacy.
Mechanics provides the scientific foundation for nearly all branches of engineering and constitutes an essential component of the education of nearly all engineering students. Through mechanics, students learn not only fundamental principles that govern the behavior of structures and machines, but they also develop the rigorous habits of mind of establishing and critiquing assumptions, translating physical problems into well-posed mathematical equations, and assessing the meaning and validity of their solutions (possibly leading to reformulation and new solutions). It is this broader understanding of mechanics that informs our holistic approach to teaching.
In a previous work6 we studied the ability of mechanics students to think critically on the basis of their ability to use of free body diagrams, use vectors, coordinates and sign conventions, and address of units and physical dimension. We discovered that about three quarters of the time, students committed some error in at least one of these areas, even if they arrived at the correct answer. We also surveyed textbooks to determine how these matters are presented, and discovered several inconsistencies and inadequacies in their treatment.
Here we present three issues – referred to as the “targeted issues” – that we believe are important to promote problem-solving skills and broader understanding of mechanics. These issues are (1) multiple-method problem-solving, in which a given problem is solved in more than one way, (2) writing equations in a standard form that is amenable to computation, and (3) careful address of assumptions. Strategies to address these issues are referred to as the “targeted strategies”.
Considering the first issue, can material be developed in a general manner such that the choice of method is presented as a fundamental part of the problem-solving process? Or must certain problems be “pigeon-holed” such that their solutions are hard-wired to only a certain approach? We probe these questions using the example of solving problems with both polar coordinates and Cartesian coordinates.
Papadopoulos, C., & Bostwick, J., & Dressel, A. (2007, June), Promoting Holistic Problem Solving In Mechanics Pedagogy Paper presented at 2007 Annual Conference & Exposition, Honolulu, Hawaii. 10.18260/1-2--3001
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